Chan Rasjid wrote:Zeno's paradox is indeed a true paradox that has no solution with certain conditions.
No motion is possible for a point to move from point A to point B. In order to reach B, it has to pass through the midpoint M; there are infinite number of midpoints to cover and so the point cannot reach point B. This is one argument that strictly has no logical flaw. I think it may be possible to find another argument that the point can also reach point B, also rigorously logical thus giving rise to a true paradox.
The reason for the true paradox is the point itself being a paradox. A point is a thing with zero space width. For a hare chasing a tortoise, the positions of the hare and tortoise are not well defined points.
EDIT: the other argument is this. If it can reach the first midpoint M, then it must have passed the midpoint of A and M; this imply that motion is possible, it can reach any point after A,etc...
Chan Rasjid.
Singapore
D_Archer wrote:Chan Rasjid wrote:Zeno's paradox is indeed a true paradox that has no solution with certain conditions.
No motion is possible for a point to move from point A to point B. In order to reach B, it has to pass through the midpoint M; there are infinite number of midpoints to cover and so the point cannot reach point B. This is one argument that strictly has no logical flaw. I think it may be possible to find another argument that the point can also reach point B, also rigorously logical thus giving rise to a true paradox.
The reason for the true paradox is the point itself being a paradox. A point is a thing with zero space width. For a hare chasing a tortoise, the positions of the hare and tortoise are not well defined points.
EDIT: the other argument is this. If it can reach the first midpoint M, then it must have passed the midpoint of A and M; this imply that motion is possible, it can reach any point after A,etc...
Chan Rasjid.
Singapore
did you read the article by Miles?
Zeno is solved, it is stated that you can reach the midway point (M), that is the start of paradox, becsuse if you can reacha midpoint you can also reach an endpoint, otherwise you would never reach the midpoint as well, because you would only reach half of the half, or half of the half of the half, ie you would not get anywhere, which is not true in reality.
Regards,
Daniel
Roshi wrote:...
Zeno's paradox: We cannot work with infinities in real world applications - like when traveling from A to B. Or when drawing a circle. A circle should not exist in the real world, because it's circumference is 2*pi*R, and that number has an infinity of decimals. Also it's radius is circumference/2*pi. It never ends to a finite determined value as we can see a circle drawn on paper.
...
There is no time:
there is only our measurement of it.
webolife wrote:Zeno's paradox is non-sense.
Once an object moves at all, it has traversed an "infinity" of points. Its motion is not impossible, OBVIOUSLY, so it is the infinity of points that is an imaginary construct. Infinity is in all its applications mathematical, not physical.
This is one reason I believe that a finite universe is the most sensible option.
neilwilkes wrote:webolife wrote:Zeno's paradox is non-sense.
Once an object moves at all, it has traversed an "infinity" of points. Its motion is not impossible, OBVIOUSLY, so it is the infinity of points that is an imaginary construct. Infinity is in all its applications mathematical, not physical.
This is one reason I believe that a finite universe is the most sensible option.
And this is why it is not quite nonsense - indeed it is very valuable.
When I was back in junior school I had a long talk with my teacher about this one (although I did not know it as Zeno's paradox then) and if memory serves it was along the lines of "are numbers infinite or not?"
The pointer to infinity is that no matter what number you can think of, I can always, always make it larger either by addition or multiplication (which is in actuality just a complex form of addition) - so to be able to touch another person - and therefore breed - however far they are away from me the distance cannot be covered because the halfway points must be infinite if numbers are infinite. A distance is 1 foot between 2 people but before they can touch they must close the distance to 6 inches, 3 inches, 1.5 inches ad nauseam. Time (which is an artificial construct created by humans to try & break things up into manageable pieces) is irrelevant here. The distance between 2 people is in theory mathematically infinite according to pure logic.
However observational evidence plainly falsifies this idea so it has to be rejected - even though pure logic and mathematics states the opposite.
Plato stated we can only understand creation (by which he presumably meant the universe) by means of pure reason and Einstein said the same - yet pure reason & mathematics can lead you badly astray.
Observation and experimental evidence is king - or should be.
Thought experiments are often misleading and no indicator of reality.
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